Small Mersenne Prime Factors (page 570/5775)

Small Mersenne Prime Factors
Prime numbers of the form M_p= 2^p − 1 are called Mersenne primes. For M_p to be prime, p must also be prime.
Any factor q of a Mersenne number 2^p − 1 must be of the form 2kp + 1, where integer k ≥ 0. Furthermore, q must be 1 or 7 mod 8.

Exp.	Prime Factor	Digits	Year
3511961	21071767	8	~1983
3511993	77263847	8	~1985
3512213	21073279	8	~1983
3512231	7024463	7	~1982
3512233	21073399	8	~1983
3512279	28098233	8	~1984
3512291	316106191	9	~1986
3512297	28098377	8	~1984
3512303	7024607	7	~1982
3512651	7025303	7	~1982
3512653	21075919	8	~1983
3512689	77279159	8	~1985
3512737	21076423	8	~1983
3512783	7025567	7	~1982
3512819	7025639	7	~1982
3512819	28102553	8
3512849	28102793	8	~1984
3512981	21077887	8	~1983
3513017	84312409	8	~1985
3513121	21078727	8	~1983
3513329	49186607	8	~1984
3513371	7026743	7	~1982
3513403	35134031	8	~1984
3513481	21080887	8	~1983
3513481	56215697	8

Exp.	Prime Factor	Digits	Year
3513527	28108217	8	~1984
3513593	21081559	8	~1983
3513701	21082207	8	~1983
3514547	28116377	8	~1984
3514649	49205087	8	~1984
3514739	7029479	7	~1982
3514799	7029599	7	~1982
3514859	7029719	7	~1982
3514939	63268903	8	~1984
3515167	35151671	8	~1984
3515669	28125353	8	~1984
3515713	105471391	9	~1985
3515783	7031567	7	~1982
3515783	84378793	8
3515819	7031639	7	~1982
3515833	21094999	8	~1983
3515903	7031807	7	~1982
3516367	56261873	8	~1984
3516389	28131113	8	~1984
3516599	7033199	7	~1982
3516749	274306423	9	~1986
3516923	7033847	7	~1982
3517313	21103879	8	~1983
3517387	140695481	9	~1985
3517421	21104527	8	~1983

Exp.	Prime Factor	Digits	Year
3517573	21105439	8	~1983
3517693	21106159	8	~1983
3517879	35178791	8	~1984
3517883	91464959	8	~1985
3517901	21107407	8	~1983
3518017	21108103	8	~1983
3518321	21109927	8	~1983
3518327	91476503	8	~1985
3518597	49260359	8	~1984
3518623	35186231	8	~1984
3518651	63335719	8	~1984
3518777	28150217	8	~1984
3518939	7037879	7	~1982
3518981	21113887	8	~1983
3519083	7038167	7	~1982
3519239	28153913	8	~1984
3519311	7038623	7	~1982
3519479	7038959	7	~1982
3519479	28155833	8
3519623	7039247	7	~1982
3519863	7039727	7	~1982
3520091	7040183	7	~1982
3520201	21121207	8	~1983
3520507	225312449	9	~1986
3520667	28165337	8	~1984

Exp.	Prime Factor	Digits	Year
3520669	77454719	8	~1985
3520669	190116127	9
3520739	7041479	7	~1982
3520927	119711519	9	~1985
3521083	35210831	8	~1984
3521117	49295639	8	~1984
3521183	7042367	7	~1982
3521281	56340497	8	~1984
3521537	49301519	8	~1984
3521723	7043447	7	~1982
3522191	28177529	8	~1984
3522479	7044959	7	~1982
3522503	7045007	7	~1982
3522763	140910521	9	~1985
3522817	21136903	8	~1983
3523519	35235191	8	~1984
3524077	246685391	9	~1986
3524197	21145183	8	~1983
3524309	28194473	8	~1984
3524537	21147223	8	~1983
3524537	28196297	8
3524537	49343519	8
3524567	28196537	8	~1984
3524767	35247671	8	~1984
3525043	35250431	8	~1984

5.471.290 digits

26-03-29